Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Congruences modulo powers of 11 for some partition functions


Author: Liuquan Wang
Journal: Proc. Amer. Math. Soc. 146 (2018), 1515-1528
MSC (2010): Primary 05A17; Secondary 11F03, 11F33, 11P83
DOI: https://doi.org/10.1090/proc/13858
Published electronically: December 4, 2017
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ R_{0}(N)$ be the Riemann surface of the congruence subgroup $ \Gamma _{0}(N)$ of $ \mathrm {SL}_{2}(\mathbb{Z})$. Using some properties of the field of meromorphic functions on $ R_{0}(11)$, we confirm a conjecture of H.H. Chan and P.C. Toh [J. Number Theory 130 (2010), pp. 1898-1913] about the partition function $ p(n)$. Moreover, we prove three infinite families of congruences modulo arbitrary powers of 11 for other partition functions, including 11-regular partitions and 11-core partitions.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 05A17, 11F03, 11F33, 11P83

Retrieve articles in all journals with MSC (2010): 05A17, 11F03, 11F33, 11P83


Additional Information

Liuquan Wang
Affiliation: School of Mathematics and Statistics, Wuhan University, Wuhan 430072, Hubei, People’s Republic of China — and — Department of Mathematics, National University of Singapore, Singapore 119076, Singapore
Email: mathlqwang@163.com; wangliuquan@u.nus.edu

DOI: https://doi.org/10.1090/proc/13858
Keywords: Partitions, congruences modulo powers of 11, regular partitions, $t$-core partitions
Received by editor(s): October 29, 2016
Received by editor(s) in revised form: June 19, 2017
Published electronically: December 4, 2017
Dedicated: Dedicated to Professor Heng Huat Chan on the occasion of his 50th birthday
Communicated by: Ken Ono
Article copyright: © Copyright 2017 American Mathematical Society

American Mathematical Society